کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155648 958754 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An Itô formula for a family of stochastic integrals and related Wong–Zakai theorems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
An Itô formula for a family of stochastic integrals and related Wong–Zakai theorems
چکیده انگلیسی

The aim of this paper is to generalize two important results known for the Stratonovich and Itô integrals to any stochastic integral obtained as limit of Riemann sums with arbitrary evaluating point: the ordinary chain rule for certain nonlinear functions of the Brownian motion and the Wong–Zakai approximation theorem. To this scope we begin by introducing a new family of products for smooth random variables which reduces for specific choices of a parameter to the pointwise and to the Wick products. We show that each product in that family is related in a natural way to a precise choice of the evaluating point in the above mentioned Riemann sums and hence to a certain notion of stochastic integral. Our chain rule relies on a new probabilistic representation for the solution of the heat equation while the Wong–Zakai type theorem follows from a reduction method for quasi-linear SDEs together with a formula of Gjessing’s type.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 123, Issue 8, August 2013, Pages 3183–3200
نویسندگان
, , ,